Texture/material mapping changes from viewport to render (p)
In response to Monster's comment I have tweaked some settings regarding UV. I found out that when I unwrapped the floors of all three types of pieces and I set the texture coordinate to UV that it looks the same for all floorpieces and also the same in the 3D view and the rendered view. 
Why it only went wrong with 1 type I still do not know (because I had not unwrapped any of the pieces earlier) but luckily the problem is solved now.